Programska aplikacija za numeričko integriranje

undergraduate thesis

• Title (english): Application Program for Numerical Integration
• Author: Grgur Radić
• Mentor: Tomislav Burić (mentor)
• Committee member: Tomislav Burić (predsjednik povjerenstva)
• Committee member: Lana Horvat Dmitrović (član povjerenstva)
• Committee member: Mirko Sužnjević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2017-07-10, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Electrical Engineering

Abstract

Cilj ovog rada bio je upoznavanje formula i algoritama za numerički izračun integrala te implementacija istih unutar aplikacije s grafičkim korisničkim sučeljem. Proučene su sljedeće metode: trapezna i Simpsonova formula te Rombergov i Gaussov algoritam. Sve metode su matematički izvedene, ostvarene programskim jezikom Java. Najvažniji isječci izvornog koda su prikazani u radu kao i rad same aplikacije na primjerima. Tako je jedan od primjera aproksimacija broja ln(2) svakom pojedinom metodom te primjer aproksimacije broja pi Rombergovim i Gaussovim algoritmom. Čitatelj pregledom umetnutih prikaza sučelja aplikacije može samostalno usporediti preciznosti pojedinih metoda.

Abstract (english)

The aim of this paper was to familiarize the formulas and algorithms for the numerical calculation of integrals and their implementation within the application with the graphical user interface. The following methods were studied: Trapezoidal rule, Simpson's rule, Romberg's method and Gaussian quadrature. All the methods are mathematically derived, implemented using Java programming language. The most important source code snippets are shown in the work as well as the application work itself in the examples. So one of the examples was approximation of the ln(2) by each particular method and the example approximating pi by Romberg's and Gaussian algorithm. The reader can recognize precision of each method by comparing the values from the application screenshots.

• Keywords: Numeričko integriranje; trapezna formula; Simpsonova formula; Rombergov algoritam; Gaussov algoritam
• Keywords (english): Numerical integration; Trapezoidal rule; Simpson's rule; Romberg's method; Gaussian quadrature
• Language: croatian
• URN:NBN: urn:nbn:hr:168:484877
• Study programme: Title: Computing; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2019-03-14 00:17:30